Problem: $\dfrac{ 6h + 4i }{ -9 } = \dfrac{ 5h - 10j }{ 4 }$ Solve for $h$.
Answer: Multiply both sides by the left denominator. $\dfrac{ 6h + 4i }{ -{9} } = \dfrac{ 5h - 10j }{ 4 }$ $-{9} \cdot \dfrac{ 6h + 4i }{ -{9} } = -{9} \cdot \dfrac{ 5h - 10j }{ 4 }$ $6h + 4i = -{9} \cdot \dfrac { 5h - 10j }{ 4 }$ Multiply both sides by the right denominator. $6h + 4i = -9 \cdot \dfrac{ 5h - 10j }{ {4} }$ ${4} \cdot \left( 6h + 4i \right) = {4} \cdot -9 \cdot \dfrac{ 5h - 10j }{ {4} }$ ${4} \cdot \left( 6h + 4i \right) = -9 \cdot \left( 5h - 10j \right)$ Distribute both sides ${4} \cdot \left( 6h + 4i \right) = -{9} \cdot \left( 5h - 10j \right)$ ${24}h + {16}i = -{45}h + {90}j$ Combine $h$ terms on the left. ${24h} + 16i = -{45h} + 90j$ ${69h} + 16i = 90j$ Move the $i$ term to the right. $69h + {16i} = 90j$ $69h = 90j - {16i}$ Isolate $h$ by dividing both sides by its coefficient. ${69}h = 90j - 16i$ $h = \dfrac{ 90j - 16i }{ {69} }$